How does the early-late correlator DLL work?

The DLL generates three copies of the local code: Early (advanced by d/2 chips), Prompt (on-time), and Late (delayed by d/2 chips), where d is the correlator spacing (typically 0.5 to 1 chip). Each copy is correlated with the received signal. The Early and Late correlator outputs represent points on the autocorrelation function slope. The error signal is |Early|^2 - |Late|^2, which is positive when the prompt is early and negative when late. This error drives a loop filter and NCO to adjust the code phase. At lock, Early and Late outputs are equal and the Prompt output is maximum. Narrower correlator spacing (d = 0.1 chip) improves multipath rejection but reduces the pull-in range.

What determines code tracking accuracy?

Tracking accuracy (jitter) depends on the signal bandwidth, C/No, loop bandwidth, and correlator spacing. The thermal noise tracking jitter for a coherent DLL is approximately: sigma_tau = sqrt(B_L * d / (2 * C/No)) chips, where B_L is the loop bandwidth in Hz and d is the correlator spacing. For GPS C/A with C/No = 45 dBHz, B_L = 1 Hz, d = 1 chip: sigma_tau ≈ 0.004 chips = 3.9 ns = 1.2 m ranging error. Reducing B_L to 0.25 Hz halves the jitter to 0.6 m. Multipath, not thermal noise, is typically the dominant error source in practice.

How does multipath affect code tracking?

A reflected signal with a small delay (0.1-2 chips) distorts the autocorrelation function, biasing the early-late discriminator and creating a ranging error of up to 150 meters for GPS C/A code. Mitigation techniques include: (1) Narrow correlator spacing (0.1 chip instead of 1 chip), reducing the maximum multipath error to about 15 meters. (2) Double-delta correlator (Strobe correlator) that uses two pairs of early-late correlators to cancel the multipath bias. (3) Multipath Estimating DLL (MEDLL) that estimates and removes individual multipath components. Modern GPS receivers achieve multipath errors below 1-2 meters in typical environments.

Signal Processing

Code Tracking

The closed-loop process that maintains sub-chip alignment between the receiver's local spreading code and the incoming signal after initial acquisition. The delay-locked loop (DLL) with early, prompt, and late correlators is the standard architecture, achieving tracking precision of 0.01 chips or better. Code tracking accuracy directly determines ranging precision in GPS (1 chip = 293 m) and code-division multiple access performance in CDMA.

Category: Signal Processing

Architecture: Delay-Locked Loop (DLL)

Precision: <0.01 chips typical

Understanding Code Tracking

After acquisition brings the code alignment within one chip, the tracking loop takes over to maintain and refine this alignment continuously. The DLL generates three time-shifted copies of the local code: Early (advanced), Prompt (on-time), and Late (delayed). The Prompt correlator output is the despreaded signal used for data demodulation. The Early and Late correlators sample the autocorrelation function on either side of the peak.

When the code alignment drifts, one side sees a larger correlation than the other. The difference (Early−Late) generates an error signal that drives the loop filter and code NCO to correct the alignment. The discriminator characteristic (S-curve) determines the loop's pull-in range and sensitivity.

DLL Tracking Equations

Early-Late Discriminator:
e = |R(τ−d/2)|² − |R(τ+d/2)|²
where R(τ) = autocorrelation, d = correlator spacing

Thermal noise tracking jitter:
σ_τ ≈ √(B_L × d / (2 × C/N₀)) chips

GPS example (C/A, C/N₀=45 dBHz, B_L=1 Hz, d=1 chip):
σ_τ = 0.004 chips = 3.9 ns = 1.2 m ranging error

Rule of thumb:
Halving B_L halves jitter. Halving d halves multipath error.

Narrow correlator (d=0.1 chip) reduces multipath error from 150 m to ~15 m.

DLL Discriminator Comparison

Discriminator	Correlator Spacing	Multipath Rejection	Noise Performance
Standard E-L	1 chip	Poor	Good
Narrow E-L	0.1 chip	Good	Slightly worse
Double-Delta	0.1 + 0.5 chip	Very good	Moderate
MEDLL	Multiple	Excellent	High complexity

Common Questions

Frequently Asked Questions

How does the early-late DLL work?

Three code replicas: Early, Prompt, Late. Error = |Early|²−|Late|². Positive when early, negative when late. Loop filter drives NCO to zero the error. At lock, Prompt output is maximum. Narrower spacing improves multipath rejection but reduces pull-in range.

What determines tracking accuracy?

Jitter ≈ √(B_L×d/(2×C/N₀)). GPS C/A at 45 dBHz, B_L=1 Hz, d=1: σ=1.2 m. Reducing B_L to 0.25 Hz halves jitter to 0.6 m. Multipath, not noise, is typically the dominant error in practice.

How does multipath affect tracking?

Reflected signals distort the autocorrelation, biasing the discriminator. Standard 1-chip spacing: up to 150 m error. Narrow correlator (0.1 chip): ~15 m. Double-delta and MEDLL techniques achieve <2 m in typical environments.

Related Terms

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